(\partial)/(\partial y)(sin(x/y))

Lösung

\frac{\partial}{\partial y} (sin (\frac{x}{y}))

- \frac{x cos ( \frac{x}{y} )}{y ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial y} (sin (\frac{x}{y}))

Behandle

x

als Konstante

Wende die Kettenregel an:

cos (\frac{x}{y}) \frac{\partial}{\partial y} (\frac{x}{y})

= cos (\frac{x}{y}) \frac{\partial}{\partial y} (\frac{x}{y})

\frac{\partial}{\partial y} (\frac{x}{y}) = - \frac{x}{y ^{2}}

= cos (\frac{x}{y}) (- \frac{x}{y ^{2}})

Vereinfache

cos (\frac{x}{y}) (- \frac{x}{y ^{2}}) : - \frac{x cos ( \frac{x}{y} )}{y ^{2}}

= - \frac{x cos ( \frac{x}{y} )}{y ^{2}}

\frac{d}{d x} (csc^{3} (3 - x))

\int \frac{8 x + 1}{( 4 x ^{2} + x ) ^{6}} d x

\frac{d}{d x} (8 7 x^{2} + 5)

\frac{d}{d x} (\frac{x}{x - 10})

\frac{d y}{d x} = \frac{2 x - 3}{5 y}